Summary
Hysteresis oscillating systems with time delay effect in feedback loop represent an object for study of the paper. The relay oscillator under consideration consists of linear system (its proper stability is uncertain) in feedback, relay hysteresis and, optionally, of an additive external action which is periodic continuous bounded function of time. Sufficient conditions are obtained for existing of asymptotically orbitally stable periodic modes of unperturbed systems and for stable periodic modes of perturbed systems. Simple analysis of perturbed periodic modes configuration is provided. An account is supported by simple illustrative examples.